4 research outputs found
The Quantum Kerr Nonlinear Coupler: The Analytical Versus Phase-Space Method
No full textThe generation of squeezed states of light in a two-mode Kerr nonlinear directional coupler (NLDC) was investigated using two different methods in quantum mechanics. First, the analytical method, a Heisenberg-picture-based method where the operators are evolving in time but the state vectors are time-independent. In this method, an analytical solution to the coupled Heisenberg equations of motion for the propagating modes was proposed based on Baker–Hausdorff (BH) formula. Second, the phase space method, a Schrdinger-picture based method in which the operators are constant and the density matrix evolves in time. In this method, the quantum mechanical master equation of the density matrix was converted to a corresponding classical Fokker-Planck (FP) equation in positive-P representation. Then, the FP equation was converted to a set of stochastic differential equations using Ito rules. The strength and weaknesses of each method are discussed. A good agreement between both methods was achieved, especially at early evolution stages and lower values of linear coupling coefficient. On one side, the analytical method seems insensitive to higher values of nonlinear coupling coefficients. Nevertheless, it demonstrated better numerical stability. On the other side, the solution of the stochastic equations resulting from the phase space method is numerically expensive as it requires averaging over thousands of trajectories. Besides, numerically unstable trajectories appear with positive-P representation at higher values of nonlinearity.The presentation of the authors' names and (or) special characters in the title of the pdf file of the accepted manuscript may differ slightly from what is displayed on the item page. The information in the pdf file of the accepted manuscript reflects the original submission by the author
Nonclassical Light in a Three-Waveguide Coupler with Second-Order Nonlinearity
No full textPossible squeezed states generated in a three-waveguide nonlinear coupler operating with second harmonic generation is discussed. This study is carried out using two well-known techniques; the phase space method (based on positive P-representation) and the Heisenberg-based analytical perturbative method. The effect of the key design parameters is analyzed for both codirectional and contra-directional propagation. The optimal degree of feasible squeezing is identified. Also, the performance and capacities of both methods are critically evaluated. For low levels of key design parameters and in the early stages of evolution, a high level of agreement between the two methods is noticed. In the new era of quantum-based technology, the proposed system opens a new avenue for utilising nonlinear couplers in nonclassical light generation
